Electrokinetic phenomena involve either the movement of charged particles through a continuous medium or the movement of a continuous medium over a charged surface. The four principal electrokinetic phenomena are electrophoresis, electroosmosis, streaming potential and sedimentation potential. These phenomena are related to one another through the zeta potential, .zeta., of the electrical double layer which exists in the neighborhood of the charged surface.
The distribution of electrolyte ions in the neighborhood of a negatively charged surface and the variation of potential, .psi., with distance from the surface are well known in the art (see, for example, Zeta Potential in Colloid Science Principles and Applications; R.J. Hunter; Academic Press, N.Y. (1988)). Two different layers of ions appear to be associated with the charged surface. The layer of ions immediately adjacent to the surface is called the inner Helmholtz (IH) layer; the second layer of ions is the outer Helmholtz (OH) layer.
Ions of the IH layer are held to the charged surface by a combination of electrostatic attraction, specific adsorption forces and chemical bonds. The thickness, .delta., of this layer is assumed to be equal to the ionic radius of the specifically adsorbed ionic species.
The second layer of ions is the OH layer. The boundary between the two layers is the limiting inner Helmholtz plane. The ions outside the OH layer are acted upon only by electrostatic forces and thermal motions of the liquid environment (Brownian motion), and they form a diffuse atmosphere of opposite charge to the net charge at the OH plane. The net charge density of the ion atmosphere of the diffused layer decreases exponentially with distance from the limiting OH plane.
The diffused layer forms one half of an electrical double layer, and the charged surface plus the inner and outer Helmholtz layers form the other half. The effective distance of separation 1/k between the two halves of the double layer is determined by the concentration of electrolyte (ionic strength). For an electrolyte of univalent ions in water at 25.degree. C. (77.degree. F.), the relationship for 1/k from the Debye-Huckel theory is described by an equation. ##EQU1## where E.sub.o is the permittivity of free space
D is the dielectric constant PA1 R is the gas constant PA1 T is the absolute temperature PA1 F is the Faraday constant PA1 I is the ionic strength, defined as: EQU I=1/2.SIGMA.(C.sub.i Z.sub.i.sup.2) (2) PA1 where, PA1 The potential .psi. on the surface of the charged particle, decreases linearly with increasing distance x in the region of the inner and outer Helmholtz layers. In the region of the diffused layer, .PHI. decreases exponentially with increasing distance x.
C.sub.i is the concentration, and PA2 Z.sub.i is the valency of the ionic species.
In electrokinetic phenomena, a displacement occurs at some plane (plane of shear) between the charged surface and its atmosphere of ions. The position of the slipping plane is known to be located in the OH layer. The potential of the plane of shear is the .zeta.-potential. From the theories of Gouy and Chapman, for spherical particles a second equation holds: ##EQU2## Where ##EQU3## q.sub.e is the charge on the particle.
Here 1/k is the effective thickness of the double layer, D the dielectric constant of the liquid, and a the particle's radius at the plane of shear. For flat surfaces, a fifth equation holds, where e is the charge per unit area of surface: ##EQU4##
Thus, the equations 2 and 3 above show that the .zeta.-potential is determined by the net charge at the plane of shear and 1/k, the effective thickness of the ion atmosphere. In turn, the .zeta.-potential controls the rate of transport between the charge surface and the adjacent liquid. The relationship between rate of transport v.sub.E and the .zeta.-potential which is valid for all four electrokinetic phenomena is given by a sixth equation, where v.sub.E is the velocity of the liquid at a large distance from the charged surface, E is the electric field strength (V/cm), and .eta. is the viscosity of the liquid. ##EQU5##
The conditions for validity of this sixth equation are that the double layer thickness (1/k) must be small compared to the radius of curvature of the surface; the substance of the surface must be nonconducting; and the surface conductance of the interface must be negligible.
The equation which relate .zeta.-potential to the streaming potential may be obtained from this sixth equation by use of Poiseuille's law for laminar flow through a capillary. For electrophoresis and sedimentation potential, v.sub.E is the velocity of the particles. E is the applied field strength for electrophoresis, whereas it is the gradient of potential developed by the sedimentation of charged particles in the sedimentation effect.
The effect of electrolyte concentration on the .zeta.-potential is also well known. Characteristically, an increase in electrolyte concentration produces a decrease in .zeta.-potential, and ions of high charge of opposite sign to that of the surface can completely reverse the sign of the .zeta.-potential. The explanation for these two effects is also well known: an increase in electrolyte concentration reduces .zeta.-potential by reducing 1/k, as indicated by equations 1-3 and 6, given above. Reversal of charge by ion adsorption occurs in the double layer and this gives rise to a .zeta.-potential of opposite sign to the original value.
Knowledge of high temperature zeta potentials and point of zero charge (pzc), as well as other physicochemical properties, is important in advanced ceramics manufacture, particle deposition, removal of charged species, coating adhesion, microbial deposition in cooling systems and in many other technologically and economically important applications where surface charge of particles plays a role.
Although .zeta.-potential measurements have been determined in the past, they have been confined to measurement at ambient temperatures or to temperatures &lt;95.degree. C. High temperature .zeta.-potential measurement has been very complex due to the high pressures involved and the difficulties associated with sample retention within the high temperature loop and its isolation from the all metal loop and the inability to measure pH at high temperatures.
Using the device of this invention, it is possible to measure zeta potentials and hence the pzc's of various oxides and other materials at high temperature and pressure. The invention is unique--no methods are currently available to determine high temperature zeta potentials of materials. The lack of a reliable method to determine the pH of aqueous systems at high temperature has prevented the experimental determination of zeta potentials.
Thus, it is an object of this invention to provide an apparatus and method for measuring .zeta.-potentials at high temperature. In a preferred embodiment, the apparatus is computer controlled.